Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Gauss map of a genus three theta divisor

Authors: Clint McCrory, Theodore Shifrin and Robert Varley
Journal: Trans. Amer. Math. Soc. 331 (1992), 727-750
MSC: Primary 14H42; Secondary 14H40, 14K25
MathSciNet review: 1070351
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Abstract: A smooth complex curve is determined by the Gauss map of the theta divisor of the Jacobian variety of the curve. The Gauss map is invariant with respect to the $ (- 1)$-map of the Jacobian. We show that for a generic genus three curve the Gauss map is locally $ {\mathbf{Z}}/2$-stable. One method of proof is to analyze the first-order $ {\mathbf{Z}}/2$-deformations of the Gauss map of a hyperelliptic theta divisor.

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Keywords: Theta divisor, Jacobian variety, Gauss map, stable map germ, infinitesimal deformation, Kodaira-Spencer map
Article copyright: © Copyright 1992 American Mathematical Society